Related papers: Learning a generalized multiscale prolongation ope…

Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we…

It is by now well-known that small adversarial perturbations can induce classification errors in deep neural networks. In this paper, we take a bottom-up signal processing perspective to this problem and show that a systematic exploitation…

We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully…

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from very few training samples. This phenomenon of data-efficiency…

Neural operators are promising surrogates for dynamical systems but when trained with standard L2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling…

It is known that the current graph neural networks (GNNs) are difficult to make themselves deep due to the problem known as over-smoothing. Multi-scale GNNs are a promising approach for mitigating the over-smoothing problem. However, there…

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…

After a more than decade-long period of relatively little research activity in the area of recurrent neural networks, several new developments will be reviewed here that have allowed substantial progress both in understanding and in…

It is well known that deep generative models have a rich latent space, and that it is possible to smoothly manipulate their outputs by traversing this latent space. Recently, architectures have emerged that allow for more complex…

During the past decade, deep neural networks have led to fast-paced progress and significant achievements in computer vision problems, for both academia and industry. Yet despite their success, state-of-the-art image classification…

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to…

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…

Consistent improvement of image priors over the years has led to the development of better inverse problem solvers. Diffusion models are the newcomers to this arena, posing the strongest known prior to date. Recently, such models operating…

Deep learning models have shown state-of-the-art performance in many inverse reconstruction problems. However, it is not well understood what properties of the latent representation may improve the generalization ability of the network.…

Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…

Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…

Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience…

Liquid composites moulding is an important manufacturing technology for fibre reinforced composites, due to its cost-effectiveness. Challenges lie in the optimisation of the process due to the lack of understanding of key characteristic of…